This document summarizes the key topics from a session on computer organization and architecture. It discusses number systems like binary, octal, hexadecimal and how to convert between them. It also covers data types that can be stored in computer registers like numbers, letters, and symbols. Binary-coded decimal and ASCII encoding schemes are introduced for representing decimal numbers and alphanumeric characters. The next session is slated to cover computer data representation through number complements.

1. CS304PC:Computer Organization
and Architecture (R18 II(I sem))
Department of computer science and engineering
(AI/ML)
Session 16
by
Asst.Prof.M.Gokilavani
VITS
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2. TEXTBOOK:
• 1. Computer System Architecture – M. Moris Mano, Third Edition,
Pearson/PHI.
REFERENCES:
• Computer Organization – Car Hamacher, Zvonks Vranesic, Safea
Zaky, Vth Edition, McGraw Hill.
• Computer Organization and Architecture – William Stallings Sixth
Edition, Pearson/PHI.
• Structured Computer Organization – Andrew S. Tanenbaum, 4th
Edition, PHI/Pearson.
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3. Unit III
Data Representation: Data types ,Complements, fixed point
Representations, Floating point representation.
Computer Arithmetic: Addition and subtraction,
multiplication Algorithms, Division Algorithms, Floating-point
Arithmetic operations, Decimal Arithmetic unit, Decimal
Arithmetic operations.
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4. Topics covered in session 16
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• Data types
• Complements
• Fixed point Representations
• Floating point representations

5. Data types
• Registers contain either data or control information
• Control information is a bit or group of bits used to specify the sequence of
command signals needed for data manipulation
• Data are numbers and other binary-coded information that are operated on
• Possible data types in registers:
o Numbers used in computations
o Letters of the alphabet used in data processing
o Other discrete symbols used for specific purposes
• All types of data, except binary numbers, are represented in binary-coded
form.
• This is because register are made up of Flip-Flops and Flip-Flops are two-
state devices that can store only 1’s and 0’s.
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6. Number systems
• A number system of base, or radix, r is a system that uses distinct symbols for r digits.
Numbers are represented by a string of digit symbols .
• Conversion of Binary to decimal: The string of digits 101101 in the binary number
system represents the quantity
1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20 = 45
(101101)2 = (45)10
• We will also use the octal (radix 8) and hexadecimal (radix 16) number systems
Conversion of Octal to decimal : (736.4)8
7 x 82 + 3 x 81 + 6 x 80 + 4 x 8-1 = (478.5)10
Conversion of hexadecimal to octal: (F3)16
F x 161 + 3 x 160 = (243)10
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7. Recap of Number System
• Convert Decimal equivalent 98 into binary Equivalent.
• Convert the following binary numbers to decimal.
i. 101110
ii. 1110101
iii. 110110100
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8. Convert Decimal equivalent 98 into binary
Equivalent .
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9. • Convert the following binary numbers to decimal.
i. 101110
ii. 1110101
iii. 110110100
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10. • Conversion from decimal to radix r system is carried out by separating
the number into its integer and fraction parts and converting each part
separately
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11. Convert decimal number 98.46 into binary
numbers.
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12. Octal to Hexadecimal number
• Each octal digit corresponds to three binary digits
• Each hexadecimal digit corresponds to four binary digits
• Rather than specifying numbers in binary form, refer to them in octal or
hexadecimal and reduce the number of digits by 1/3 or ¼, respectively.
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15. Question
Convert the following decimal number to the
bases indicated
a. 7562 to octal
b.1938 to hexadecimal
c. 175 to binary
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16. Decimal representation
• Numerous different codes can be obtained by arranging four
bits in 10 distinct combinations.
• Binary-coded decimal (BCD) is a class of binary encodings
of decimal numbers where each digit is represented by a fixed
number of bits, usually four or eight.
• Sometimes, special bit patterns are used for a sign or other
indications (E.g: error or overflow). This particular code is
called binary coded decimal and commonly know as BCD.
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18. BCD
• A binary code is a group of n bits that assume up to 2n distinct
combinations
• A four bit code is necessary to represent the ten decimal digits – 6 are
unused
• The most popular decimal code is called binary-coded decimal (BCD)
• BCD is different from converting a decimal number to binary
• For example 99, when converted to binary, is 1100011
• 99 when represented in BCD is 1001 1001
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19. Question
1. Convert Decimal Equivalent 278 to BCD
number.
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21. Question
1.
2.
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22. ASCII
• The standard alphanumeric binary code is ASCII
• This uses seven bits to code 128 characters
• Binary codes are required since registers can hold binary information
only
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24. Question
1.
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25. Topics to be covered in next session 17
• Complements
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Thank you!!!